Methodologies / fx-var-es
Value-at-Risk and Expected Shortfall
Historical left-tail quantile and Gaussian parametric VaR/ES on user P&L.
Formula
Hist VaR = −Q_α(PnL); ES = −mean(PnL | PnL ≤ Q_α); Param VaR = −(μ+σΦ⁻¹(α))
Assumptions
- Observations are i.i.d. P&L (parametric normality for that method).
- Negative P&L is a loss; reported VaR/ES are loss amounts.
Limitations
- Not a regulatory capital model.
- Small samples and non-normal FX returns make estimates unstable.
- Does not scale P&L to a holding period; the series must already be at the stated horizon.